I am trying to install a build of Chromium OS on my PC. I do not have any spare disks or flash drives. I want to find a way from installing the .iso from Ubuntu Live CD. How would I go about doing this? My friend suggested mounting the .iso, but I don't know what he's talking about.

potentially you could use QEMU to attach your real harddisk inside a virtual instance booted off that .iso you are willing to install. can be a bit tricky but it worked for me.

once booted from Ubuntu Live CD install qemu:

sudo apt-get install qemu

then download Chromium OS iso.
run QEMU telling it to boot off the .iso and use your real harddisk.

sudo qemu -drive file=/tmp/chromium-install.iso,if=ide,index=1,media=cdrom -hda /dev/sda[add partition number if you want to use one]

i have to warn you though that this might screw things up. you would be safer off by only using a partition of the harddisk dedicated for the install of Chromium OS. you might need to do some bootloader configuration if you consider installing on a partition.